Stability of an auto catalytic system under noise perturbations and its dependence on the basin of attraction

Liu, J. and Crawford, J. W. (1997) Stability of an auto catalytic system under noise perturbations and its dependence on the basin of attraction. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 453(1961), pp. 1195-1203. (doi: 10.1098/rspa.1997.0066)

Abstract

The stability of an autocatalytic system subject to noise perturbations is investigated. It is found that for non-fractal basins, noise always induces a transition from the stable focus to the stable node in the system. A critical amplitude is defined as the minimum standard deviation in Gaussian-distributed noise required to induce a transition in a prescribed interval of time. For non-fractal basins, the logarithm of the critical amplitude depends linearly on the area of the basin of attraction. As the bifurcation parameter approaches the interval corresponding to chaotic behaviour, a marked deviation from linear dependence is observed. Subsequent to the emergence of chaotic dynamics, the basin of attraction becomes fractal. On changing from a non-fractal to a fractal basin by a continuous change in the bifurcation parameter, the critical amplitude is discontinuously reduced. From these results, it is concluded that the basin of attraction of a dynamical state, rather than the dynamical patterns of that state, determines its stability.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Crawford, Professor John
• Authors: Liu, J., and Crawford, J. W.
• College/School: College of Social Sciences > Adam Smith Business School > Management
• Journal Name: Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
• Publisher: The Royal Society
• ISSN: 1364-5021
• ISSN (Online): 1471-2946